➗ Math
Percentages Made Simple: Three Formulas That Cover Everything
Almost every percentage question is one of three types. Learn the three formulas — percentage of a number, one number as a percentage of another, and percentage change — with worked examples.
Updated 20 August 2026 · 2 min read
Percentages feel slippery because the same word covers several different questions. The good news: almost everything you'll ever need falls into just three types. Learn one formula for each and you can handle tips, discounts, tax, test scores and price changes without reaching for a rule you half-remember.
1. Finding a percentage of a number
This is the classic "what is 15% of 80?" question. Convert the percentage to a decimal (divide by 100) and multiply:
This is the maths behind tips, sales tax and simple discounts. If a £80 jacket is 15% off, the discount is £12 and you pay £68. You can check any of these instantly with the percentage calculator or, for shopping specifically, the discount calculator.
2. One number as a percentage of another
Here the question flips: "12 is what percent of 80?" Divide the part by the whole, then multiply by 100:
This is how you turn a test score of 47 out of 60 into a percentage (47 ÷ 60 × 100 ≈ 78.3%), or work out what share of your budget a bill takes up.
3. Percentage change (increase or decrease)
This one trips people up the most. To measure how much a value has moved — a price rise, a pay increase, a drop in visitors — compare the change to the starting value, not the new one:
A positive result is an increase, a negative one a decrease. Our percentage change calculator does this both ways and shows the absolute change too.
The trap: percentages don't add up
Two things people get wrong constantly:
- A percentage change and its reverse aren't equal. A price that rises 25% then falls 25% does not return to where it started — it ends up 6.25% lower, because the second 25% is taken from a bigger number.
- Stacked discounts don't sum. 25% off followed by an extra 10% off is 32.5% off in total, not 35%. The second discount applies to the already-reduced price.
- Percentage points aren't percentages. Going from 10% to 15% is a 5 percentage-point rise, but a 50% increase.
Keep these three formulas in your back pocket and the rest is just plugging in numbers. When you'd rather not do it by hand, the percentage calculator covers all three in one place.
Frequently asked questions
- What's the quickest way to work out a percentage in your head?
- Find 10% first by moving the decimal point one place left, then scale it. 10% of 80 is 8, so 5% is 4 and 15% is 12. Most everyday percentages can be built from 10%, 5% and 1%.
- How do I reverse a percentage — find the original price before a discount?
- Divide by (1 minus the discount as a decimal). If an item costs £60 after 25% off, the original was 60 ÷ 0.75 = £80.